The multi-dimensional truncated moment problem: maximal masses (Q2822215)

Let \(\mathcal K\subset \mathbb R^d\), \(L\) be a linear functional on the set \(\mathbb R^d_{2n}[x]\), \(x=(x_1,\ldots ,x_d)\), of all polynomials of degrees \(\leq 2n\). A functional \(L\) is called a truncated \(\mathcal K\)-moment functional if there exists a positive regular Borel measure \(\mu\) on \(\mathbb R^d\) supported by \(\mathcal K\), such that NEWLINE\[NEWLINE L(p)=\int p(x)\,d\mu (x),\quad p\in \mathbb R^d_{2n}[x]. NEWLINE\]NEWLINE The set of such measures is denoted by \(\mathcal M_{L,\mathcal K}\). Let \(\operatorname{Pos}(\mathcal K)_{2n} = \{ p\in \mathbb R^d_{2n}[x] : p(x)\geq 0 \text{ for }x\in \mathcal K\)